Finite-Time Observer-Based $H_{\infty }$ Fault-Tolerant Output Formation Tracking Control for Heterogeneous Nonlinear Multi-Agent Systems

This paper investigates the robust
$H_{\infty }$
fault-tolerant output time-varying formation tracking (TVFT) problem for heterogeneous nonlinear multi-agent system, whose object is that the outputs of followers need to track leader's output and achieve the desired formation under the influences of actuator faults and external disturbances. In order to derive the leader's information including state, system matrices, and the upper bound of the unknown input, two kinds of distributed finite-time observers are presented for each follower, respectively, which removes the assumption that this information is derived by all agents directly in previous studies. Then, a novel adaptive
$H_{\infty }$
fault-tolerant output TVFT controller is developed to make up for the parameter uncertainties, actuator faults and leader's unknown input. Moreover, with the help of Lyapunov theory and the linear matrix inequality technique, the robust
$H_{\infty }$
output TVFT criterion for the considered multi-agent system subject to the leader's unknown input and actuator faults is obtained based on the presented distributed adaptive
$H_{\infty }$
output TVFT controller. Finally, a simulation example is given to demonstrate these derived theoretical results.